It has been proved in [1]} that
the equation (REF ) satisfies the maximum bound principle (MBP) in the sense that
if the absolute value of the initial data is bounded pointwise by \(\beta \) ,
then the absolute value of the solution is also bounded by \(\beta \)  pointwise for all time, i.e.,
\(\max _{\mathbf {x}\in \overline{\Omega }} |u_{\text{\rm init}}(\mathbf {x})| \le \beta \quad \Longrightarrow \quad \max _{\mathbf {x}\in \overline{\Omega }} |u(t,\mathbf {x})| \le \beta , \quad \forall \, t > 0.\) 
